Simplify ((5s^3n^2)^-1)/(4s^3)

$\frac{{(5 s^{3} n^{2})}^{- 1}}{4 s^{3}}$

Move ${(5 s^{3} n^{2})}^{- 1}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{4 s^{3} (5 s^{3} n^{2})}$

Multiply $s^{3}$ by $s^{3}$ by adding the exponents.

Move $s^{3}$ .

$\frac{1}{4 (s^{3} s^{3}) (5 n^{2})}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{1}{4 s^{3 + 3} (5 n^{2})}$

Add $3$ and $3$ .

$\frac{1}{4 s^{6} (5 n^{2})}$

Multiply $5$ by $4$ .

$\frac{1}{20 s^{6} n^{2}}$